Wafaa Batat

The Lorentzian oscillator group as a geodesic orbit space

We prove that the four-dimensional oscillator group Os, endowed with any of its usual left-invariant Lorentzian metrics, is a Lorentzian geodesic (so, in particular, null-geodesic) orbit space with some of its homogeneous descriptions corresponding to certain homogeneous Lorentzian structures. Each time that Os is endowed with a suitable metric and an appropriate homogeneous Lorentzian structure, it is a candidate for constructing solutions in d-dimensional supergravity with at least 24 of the 32 possible supersymmetries.

A survey on homogeneous structures on the classical hyperbolic spaces

This is a survey on homogeneous Riemannian, Kahler or quaternionic Kahler structures on the real, complex or quaternionic hyperbolic spaces \(\mathbb {R}\mathrm {H}(n)\), \(\mathbb {C}\mathrm {H}(n)\) and \( \mathbb {H}\mathrm {H}(n)\), respectively.

On the Existence of a Codimension 1 Completely Integrable Totally Geodesic Distribution on a Pseudo-Riemannian Heisenberg Group

In this note we prove that the Heisenberg group with a left-invariant pseudo- Riemannian metric admits a completely integrable totally geodesic distribution of codimen- sion 1. This is on the contrary to the Riemannian case, as it was proved by T. Hangan.